Local Tomography and the Jordan Structure of Quantum Theory

Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection rules is the only non-signaling probabilistic theory in which (i...

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Bibliographic Details
Published inFoundations of physics Vol. 44; no. 2; pp. 192 - 212
Main Authors Barnum, Howard, Wilce, Alexander
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.02.2014
Subjects
Classical and Quantum Gravitation
Classical Mechanics
History and Philosophical Foundations of Physics
Philosophy of Science
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Statistical Physics and Dynamical Systems
General probabilistic theories
Jordan algebras
Local tomography
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Summary:Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection rules is the only non-signaling probabilistic theory in which (i) individual systems are Jordan algebras (equivalently, their cones of unnormalized states are homogeneous and self-dual), (ii) composites are locally tomographic (meaning that states are determined by the joint probabilities they assign to measurement outcomes on the component systems) and (iii) at least one system has the structure of a qubit. Using this result, we also characterize finite dimensional quantum theory among probabilistic theories having the structure of a dagger-monoidal category.
ISSN:0015-9018
1572-9516
DOI:10.1007/s10701-014-9777-1